Abstract :
Let F be a field of characteristic ≠2, V a non-singular 2n-dimensional symplectic space over F, v1,v2,…,v2n a basis for V, and Spn(F) the collection of symplectic isometries of V with respect to this basis. We consider the following completion question: If A is any n×n F-matrix, must there be some Dset membership, variantSp2n(F) withimageIt is shown that for some particular important choices of bases, the answer is yes, but it does not hold in general.
